009A Sample Final 3, Problem 7

Compute

a) $\lim _{x\rightarrow 0}{\frac {x}{3-{\sqrt {9-x}}}}$

b) $\lim _{x\rightarrow \pi }{\frac {\sin x}{\pi -x}}$

c) Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \lim_{x\rightarrow -2} \frac{x^2-x-6}{x^3+8}}

Foundations:

Solution:

(a)

Step 1:

Step 2:

(b)

Step 1:

Step 2:

(c)

Step 1:

Step 2:

Final Answer:
(a)
(b)
(c)

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